Consider the following subsets of R³ and • decide if they are vector subspaces • if they are vector subspaces, find a basis • if they are vector subspaces, find the dimension (a) {(a, b, a – b) | a, b E R} (b) {(a, a, a²) | a € R} (c) {(x, y, 2) | x + 3y – z = 0} (d) {(x,y, z) | x + 3y – z = 1}

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A: Given that W1 and W2 are two subspace of a vector space V over a field F.

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Q: i) Determine the linear mapping T : R3 → R² which maps the basis vectors {(1,0,0), (0, 1,0), (0,0,…

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Q: Q4. Simplify the following expression: 3-5 x 39 Click on image to enlarge if needed 12 81 243 324

A: To evaluate :- 3-5 * 39

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A: The solution is given as

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